Bentham's founding move was to sweep away everything that could not be cashed out in experience. Tradition, natural rights, divine command — none of these, he thought, gave a reason anyone could inspect. What can be inspected is whether an action makes conscious beings better or worse off. So make that the whole of morality, and the rest becomes calculation.
He meant calculation fairly literally, proposing a felicific calculus that weighed pleasures and pains by intensity, duration, certainty, and how many were affected. And he drew the impartiality consequence without flinching: each person counts for one and nobody for more than one, regardless of rank. That was politically radical in the eighteenth century, and it also carried an implication Bentham accepted directly — that the capacity to suffer, not the capacity to reason or speak, is what qualifies a creature for moral consideration. This is why utilitarianism became the natural home of animal ethics.
Mill inherited the theory and immediately repaired its weakest point. Critics complained that a philosophy of pleasure was fit for swine. Mill's response distinguished higher from lower pleasures: those engaging our distinctively human capacities are more valuable in kind, not merely in quantity, and the verdict of people who have experienced both is the test. Critics have argued ever since that this smuggles in a standard beyond pleasure, since if quality trumps quantity then something other than pleasure is doing the ranking.
The objectionsWhere the theory strains.
Justice. The best-known objection: if punishing an innocent person would prevent a riot and save lives, utilitarianism appears to require it. Any theory that judges only by aggregate outcome can in principle sacrifice an individual for a larger sum, and no reformulation has fully removed that possibility.
Demandingness. If your wellbeing counts exactly as much as a stranger's, then almost any luxury you buy is money you could have used to relieve serious suffering elsewhere. Peter Singer has pressed this consistently and accepted the conclusion. Most people regard a theory that condemns nearly every ordinary life as having gone wrong somewhere — though "that's too demanding" is a complaint about comfort, not obviously an argument.
Integrity. Bernard Williams argued that utilitarianism alienates people from their own commitments. If the calculation says you must abandon a project central to your identity, the theory treats that as a straightforward matter of arithmetic — which misdescribes what it is to be a person with a life of your own.
Calculation. We cannot actually predict consequences reliably, or compare wellbeing across people. Defenders reply that this is a practical difficulty rather than a flaw in the criterion, and that rules of thumb handle most cases well.
Rule utilitarianism answers several of these by shifting the assessment to rules whose general acceptance maximises wellbeing — under which framing the innocent should not be punished, because a practice of doing so would be catastrophic. The standing objection is that a rule utilitarian who genuinely follows a rule when breaking it would produce more good has stopped being a utilitarian, and one who breaks it has collapsed back into act utilitarianism.